Optimizing Stick Rotation in Space: Ideal Center of Mass Placement

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Discussion Overview

The discussion revolves around the optimal placement of the center of mass (COM) of a stick in space to maximize the backward rotation of one end when a force is applied to the opposite end. Participants explore various configurations and the implications of mass distribution on motion, considering both theoretical and practical aspects.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants assert that for a uniform stick, the center of mass is at the midpoint (5 cm), and any push will result in motion and rotation about this point.
  • Others question the implications of having the center of mass offset, suggesting that different configurations could lead to varying rotational dynamics.
  • A participant proposes a scenario with three sticks having different center of mass placements, seeking to determine which configuration would yield the most backward motion of one end when pushed.
  • Some participants explore the effects of mass distribution, suggesting that concentrating mass at one end may enhance backward acceleration of the opposite end.
  • There is a discussion about the relationship between torque, mass distribution, and resultant velocities, with some participants expressing uncertainty about the calculations involved.
  • Participants express differing views on whether the ideal position of the center of mass is at the midpoint or closer to the end where the force is applied, with some suggesting that a closer position may yield faster rearward acceleration.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the optimal position of the center of mass. There are multiple competing views regarding the effects of mass distribution and the resulting motion of the stick, indicating an unresolved discussion.

Contextual Notes

Participants mention the need to calculate torque and resultant velocities, but the specific mathematical steps and assumptions involved remain unresolved. The discussion also highlights the complexity of the problem, with varying interpretations of the center of mass and its implications for motion.

Who May Find This Useful

This discussion may be of interest to those studying physics, particularly in areas related to mechanics, rotational dynamics, and mass distribution effects on motion.

  • #31
jbriggs444 said:
The original question is not well enough posed to have a definite answer. But yes, for a reasonable understanding of the intended question, the answer is "the middle".
PeroK put it way better than I did:When you give an impulse to one end of the rod, the COM moves forward and the object rotates around the COM. The initial velocity of the other end if the rod is the sum of the forward velocity of the COM and a backwards velocity from the rotation.

Question: what mass distribution will result in the other end of the rod initially moving backwards from its starting position with the greatest speed?
 
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  • #32
Erunanethiel said:
Question: what mass distribution will result in the other end of the rod initially moving backwards from its starting position with the greatest speed?
Answer: undefined. There is no optimum. The distribution with all of the mass exactly in the center results in an undefined speed and, accordingly, is ineligible.
 
  • #33
jbriggs444 said:
Answer: undefined. There is no optimum. The distribution with all of the mass exactly in the center results in an undefined speed and, accordingly, is ineligible.
Do you mean that the location of center of mass does not matter for this, the only thing that does is how "centralized" the mass is to CoM, irrespective of it's location. In short: Make every where that is not CoM make as light as possible.

Correct?
 
  • #34
Erunanethiel said:
Do you mean that the location of center of mass does not matter for this, the only thing that does is how "centralized" the mass is to CoM, irrespective of it's location. In short: Make every where that is not CoM make as light as possible.
The location of the center of mass relative to the ends matters. But so does the degree to which the mass is centralized. Both are relevant. One can even write an equation.

Try it. Apply an impulse "p" at right angles to one end of a rod of length "l" and mass "m" with center of mass offset "r" from the end where the impulse will be applied. If the rod has a moment of inertia "I", what speed will the other end have as a result?

Edit: Take it a step at a time. For instance, what rotation rate will result from the applied impulse?
 
  • #35
jbriggs444 said:
Answer: undefined. There is no optimum. The distribution with all of the mass exactly in the center results in an undefined speed and, accordingly, is ineligible.
Well, not that the other bits have no mass, they are as I said made as light as possible
 
  • #36
jbriggs444 said:
The location of the center of mass relative to the ends matters. But so does the degree to which the mass is centralized. Both are relevant. One can even write an equation.

Try it. Apply an impulse "p" at right angles to one end of a rod of length "l" and mass "m" with center of mass offset "r" from the end where the impulse will be applied. If the rod has a moment of inertia "I", what speed will the other end have as a result?

Edit: Take it a step at a time. For instance, what rotation rate will result from the applied impulse?
If the location of the center of mass relative to the ends matters, would the optimum position be in the middle, or closer to the side which the force is applied?
 
  • #37
Erunanethiel said:
If the location of the center of mass relative to the ends matters, would the optimum position be in the middle, or closer to the side which the force is applied?
Sorry, you are going to have to put some effort of your own into this problem. Until you do, I'm out.
 

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